Question

Mike and Ken shared some stamps. \frac{1}{5} 5 1 ​ of Ken's stamps were \frac{1}{3} 3 1 ​ of Mike's stamps. If Mike gave Ken 24 stamps, Ken would have thrice as many stamps as Mike. Find the number of stamps each of them had in the beginning.

Answer 1

Mike had 72 stamps

Ken had 120 stamps

Explanation:

Given

`M \to Mike`

`K \to Ken`

`(1)/(5) * K = (1)/(3) * M`

`K + 24 = 3 * ( M - 24)`

Required

Find K and M

Make K the subject in:
`K + 24 = 3 * ( M - 24)`

`K = 3 * ( M - 24) - 24`

Substitute
`K = 3 * ( M - 24) - 24` in
`(1)/(5) * K = (1)/(3) * M`

`(1)/(5) * [3 * ( M - 24) - 24] = (1)/(3) * M`

Open brackets

`(1)/(5) * [3M - 72 - 24] = (1)/(3) * M`

`(1)/(5) * [3M -96] = (1)/(3) * M`

Multiply both sides by 15

`3* [3M -96] = 5 * M`

`9M -288 = 5M`

Collect like terms

`9M -5M= 288`

`4M= 288`

Divide both sides by 4

`M= 72`

Substitute
`M= 72` in
`K = 3 * ( M - 24) - 24`

`K = 3 * (72 - 24) - 24`

`K = 3 * 48 - 24`

`K = 120`